I first met Gian-Carlo when I was a graduate student at Harvard in 1967. At that time I regarded combinatorics as a "Mickey Mouse" subject and could not conceive of doing serious research in that area. However, I became interested in a combinatorial problem related to some other work, and it was suggested that I talk to a "Professor Rota" at MIT. I was at once infected by his enthusiasm for combinatorics and his new way of approaching the subject. From that point combinatorics became my main mathematical interest. Gian-Carlo has subsequently played a major role in every step of my career, from my first job as a Moore Instructor at MIT to my eventual tenure, with various honors and awards along the way. Throughout my entire career he has remained my closest colleague and a wonderful friend.
My experience with Gianco is hardly unique. The huge number of people here today is a testimony to that. He captivated everyone who knew him with his charm, concern, and respect, and he inspired countless students and colleagues to achieve their maximum potential.
Gian-Carlo's interest in combinatorics developed after he received his doctoral degree in the completely different field of functional analysis. He intuitively realized that combinatorics, which at that time was a rather disreputable and poorly organized area, had a tremendous potential to rise to the level of such elite mathematical subjects as algebraic geometry and number theory. It is this type of intuitive understanding that was characteristic of Gianco's work - he was always looking for the "big picture and trying to understand the true essence of any subject in which he was interested. It is hard for young combinatorialists today to imagine what it was like in Cambridge in the late 1960's and early 1970's when combinatorics was finally being put on a firm foundation. Breakthroughs in understanding led to the planting of many seeds which subsequently blossomed into vast subjects of their own, such as topological combinatorics, the combinatorial theory of symmetric functions, and matroid theory. Many of these breakthroughs were first brought to light in Gian-Carlo's seminar called "Syzygy Street," which has now evolved into the twice-weekly MIT Combinatorics Seminar.
An important watershed in the development of combinatorics was the National Science Foundation Advanced Science Seminar in Combinatorial Theory at Bowdoin College in Brunswick, Maine, during the summer of 1971. Gian-Carlo presided over this meeting as a godfather of the "new combinatorics." He was involved in all aspects of the eight-week meeting, from the mathematical content to social activities. I recall one amusing innovation of his - the tandem lecture. He chose about six people from the audience who had to leave the room and not talk to each other. He would call the people into the lecture hall one at a time to deliver a five-minute lecture. The lecture had to be a continuation of the previous speaker's lecture, based on what the previous speaker left on the blackboard. The speakers were not allowed to erase their own writing from the board.
This is not the proper occasion to discuss details of Gian-Carlo's mathematical accomplishments, but I should mention his series of papers with the audacious title "On the Foundations of Combinatorial Theory." The first paper in this series, published in 1964, established partially ordered sets as a fundamental concept in combinatorics. It had a tremendous influence on the development of combinatorics that continues unabated to this day. Other areas in which Gian-Carlo made major contributions include matroid theory, finite operator calculus (which was a brilliant revival of the moribund nineteenth century subject of umbral calculus), Hopf algebras, symmetric functions and the symmetric group, and classical invariant theory. All this work was characterized by a unique blend of originality, synthesis, and elegance that only Gian-Carlo could achieve.
Being associated with Gian-Carlo meant far more than attending classes and seminars. He became an important part of your personal life. He took a genuine interest in the well-being of all his associates and made many selfless sacrifices of time, money, and intellectual effort on their behalf. It goes without saying that this altruism, together with his beautifully prepared and delivered lectures, made him one of the most popular and respected teachers at MIT. I am sure that others at this gathering will say more about this aspect of Gian-Carlo's career.
There were many other facets of Gian-Carlo's complex personality that I will also leave to others. These include his deep interest in phenomenology, his completely honest and lucid essays on mathematicians and the practice of mathematics, his many editorial projects and related book reviews, his visiting and consulting positions throughout the world, especially at Los Alamos Scientific Laboratories beginning in 1966, and the parties at his old apartment in Charles River Park with a bathtub full of ice and champagne bottles and featuring hot chili pepper eating contests.
Gian-Carlo gathered many honors and awards throughout his career. To name just a few, he received four honorary degrees (and was just about to receive another from Nankai University). He was awarded the Steele Prize of the American Mathematical Society in 1988 and the James R. Killian Faculty Achievement Award at MIT in 1996. He was appointed the Norbert Wiener Professor of Mathematics at MIT for a five-year period beginning in 1998, and he was the Colloquium Lecturer of the American Mathematical Society in 1998.
I had two long conversations with Gian-Carlo during the last week of his life. The main topic was his plans for the future. He was overflowing with ideas and designs. He mentioned several intriguing mathematical projects. He was debating whether to write an essay that would be certain to alienate a certain distinguished mathematician. He tried to persuade me to move to a vacant condo in the building in which he lived so we could discuss mathematics on a regular basis in the cafés of Harvard Square. After preparing this talk, the first thought that popped into my mind was to show it to Gianco and obtain his approval. It will not be easy to adjust to his absence.